Coulomb's Law - General Physics Lecture

Overview

• Coulomb's Law provides the formula for the electrostatic force between two point charges.
• It's related to one of the four fundamental forces.
• Relevant for solving mechanics problems in 1 and 2 dimensions.

Formula

• Coulomb's Law: F = K \( \frac{|q1 , q2|}{r^2} \)
  • K: Coulomb constant = 8.99 x 10^9 N m^2/C^2
  • |q1|, |q2|: magnitudes of the charges in coulombs
  • r: distance of separation in meters

Important Concepts

• Electrostatic Force

  • Attractive: Between opposite charges (one positive, one negative)
  • Repulsive: Between like charges (both positive or both negative)

• Comparison to Gravity

  • Gravitational Force: Always attractive
  • Electrostatic Force: Can be either attractive or repulsive

Proportionality

• Force is proportional to the magnitude of each charge:
  • Doubling q1 or q2 doubles F
  • Doubling both q1 and q2 quadruples F
• Force is inversely proportional to the distance squared:
  • Doubling the distance reduces F by a factor of 4

Practical Example 1

• Given: Two point charges, each 1 C, 0.1 m apart
• Find: Electrostatic force
  • F = 8.99 x 10^9 \( \frac{(1 , C) , (1 , C)}{(0.1 , m)^2} \)
  • F ≈ 8.99 x 10^11 N

Practical Example 2

• Revised: Two point charges, each 1 μC, 0.1 m apart
• Calculation
  • Convert μC to C: 1 μC = 1 x 10^-6 C
  • Use same formula:
  • F ≈ 8.99 x 10^-1 N

Two-Dimensional Problem

• Find: Magnitude and direction of net electrostatic force on a charge
• Setup: Three charges interaction, calculate forces, use vector addition
• Sample Calculation
  • Charges: +2 μC, -1 μC, +4 μC
  • Distance: 1 μC apart
  • Forces: Calculate for each pair, use Pythagorean theorem and trigonometric functions

Mechanics Problem

• Given: Two spheres, each 1 g, 10 cm strings, 30° from the vertical
• Find: Magnitude of charge
• Process
  • Draw free body diagram
  • Use sum of forces equations
  • Calculate tension
  • Use Coulomb’s Law to find charge magnitude
• Calculation
  • T = mg/sin(60°)
  • Solve for Q using rearranged Coulomb's equation
  • Result: Q ≈ 7.9 x 10^-8 C

Tips

• Use consistent units (e.g., convert μC to C)
• Remember to square the distances in Coulomb's Law formula
• Vector addition is key for multi-dimensional problems
• Breakdown problems step-by-step for clarity

Resources

• Chad's Prep (channel and website)
• Premium courses, practice problems, and study guides available

Happy studying!